Étude des relations algébriques entre les racines d'un polynôme d'une variable

@article{Valibouze1999tudeDR,
  title={{\'E}tude des relations alg{\'e}briques entre les racines d'un polyn{\^o}me d'une variable},
  author={Annick Valibouze},
  journal={Bulletin of The Belgian Mathematical Society-simon Stevin},
  year={1999},
  volume={6},
  pages={507-535}
}
  • Annick Valibouze
  • Published 1999
  • Mathematics
  • Bulletin of The Belgian Mathematical Society-simon Stevin
Cet article developpe une vision effective de la theorie de Galois algebrique en apportant des proprietes inherentes aux ideaux associes a un polynome d’une variable. Il debouche sur un algorithme de calcul du groupe de Galois d’un polynome et de l’ideal des relations entre ses racines. 
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References

SHOWING 1-10 OF 55 REFERENCES
Calculs d'invariants primitifs de groupes finis
TLDR
Two algorithms are presented, the first one enable us to calculate all primitive invariant of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. Expand
Formal Computation of Galois Groups with Relative Resolvents
TLDR
A systematic and formal method to compute the Galois group of a non-necessarily irreducible polynomial, based on a formal method of specialization of relative resolvents, which reduces the problem to that of specializing a primitive element. Expand
Using Galois Ideals for Computing Relative Resolvents
TLDR
It is shown that some ideals which occur in Galois theory are generated by triangular sets of polynomials, and this property enables a new algebraic method for computing relative resolvents which works with any polynomial invariant. Expand
Computation of the splitting fields and the Galois groups of polynomials
This study is a continuation of Yokoyama et al. [22], which improved the method by Landau and Miller [11] for the determination of solvability of a polynomial over the integers. In both methods, theExpand
A new efficient algorithm for computing Gröbner bases (F4)
This paper introduces a new efficient algorithm for computing Grobner bases. To avoid as much intermediate computation as possible, the algorithm computes successive truncated Grobner bases and itExpand
Solutions of Systems of Algebraic Equations and Linear Maps on Residue Class Rings
TLDR
It is found that many ideal-theoretical arguments for the problem can be translated into their counterparts in the theory of linear maps and this translation succeeds in giving a new description for the U-resultant and forms of solutions of systems straightforwardly. Expand
On invariant polynomials and their application in field theory
Certain polynomials invariant under a permutation group G (so called G-polynomials) play an important role in several computational methods of Galois theory. Since their practical value depends onExpand
Computing subfields: Reverse of the primitive element problem
We describe an algorithm which computes all subfields of an effectively given finite algebraic extension. Although the base field can be arbitrary, we focus our attention on the rationals.
Symbolic Computation with Symmetric Polynomials an Extension to MACSYMA
TLDR
This package, called SYM, constitutes at present an extension of the system of symbolic computation MACSYMA that performs a few manipulations on symmetric polynomials and can be used for direct applications and some algorithms extend easily to functions that are symmetric with respect to sets of variables. Expand
Computing Galois groups over the rationals
Abstract Practical computational techniques are described to determine the Galois group of a polynomial over the rationals, and each transitive permutation group of degree 3 to 7 is realised as aExpand
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